Now, with reasonable descriptions of low-lying meson masses at \(|eB| \lesssim 0.15\, {\rm GeV}^2\) ,
we examine the low temperature thermodynamics.
Shown in Fig.REF  are the entropy densities of a neutral meson gas for various \(B\)  and \(T\) .
We plot the results for the neutral mesons (\(s_{\rm n}^{\rm R}\) ), neutral plus charged mesons (\(s_{\rm n+ch}^{\rm R}\) ) with relativistic corrections,
and \(s_{\rm n+ch}^{\rm NRQ}\)  within pure non-relativistic treatments.
They are compared with the lattice results in Ref.[1]}.
As a guideline we also plot the HRG result at \(B=0\)  which is based on the PDG list for mesonic and baryonic
spectraIn
Ref.[2]}, the author computed the PDG based HRG entropy at finite \(B\) , regarding hadrons as elementary particles.
The resulting entropy density to \(T \sim 100\)  MeV is found to be very close to the \(B=0\) ..
As we have mentioned before, our HRG includes only mesons and the resulting entropy should be smaller than in the lattice.
The baryon masses are \(\gtrsim 0.9\)  GeV, so we expect the corrections become substantial for \(T\gtrsim 100\)  MeV.
